Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
376 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 141 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C7×#544 | C2 | semidirect |
| 3. #89866 | C2 | semidirect |
| 4. #89856 | C2 | semidirect |
| 5. #89838 | C2 | semidirect |
| 6. #89835 | C2 | semidirect |
| 8. #89771 | C2 | semidirect |
| 9. #89767 | C2 | semidirect |
| 11. C2×#6382 | C2 | semidirect |
| 48. #1157 | Q8 | semidirect |
| 76. #544 | D7 | semidirect |
| 224. C7 | #3084 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#544 | 2 |
| #90214 | 2 |
| #89866 | 2 |
| #89856 | 2 |
| #89838 | 2 |
| #89835 | 2 |
| #89774 | 2 |
| #89771 | 2 |
| #89767 | 2 |
| #89738 | 2 |
| C2×#6382 | 2 |
| #3084 | 7 |